Heat up about 2/3 of the milk with the vanilla seed and its scraped pod on medium heat.
Place egg yolks, corn starch and sugar in a bowl, add the remaining 1/3 of the milk and whisk until smooth.

When the milk is simmering, ladle/pour a little by little of the hot milk to the egg yolk mixture about 1/4 at a time, whisking as you add the milk, when mixture is homogenized. Pour everything back into the pot.

Keep whisking until it reaches a boil. Take off heat and strain it into a container. Cover with plastic wrap, the wrap should be touching the surface of the pastry cream. Let cool and chill until ready to use.

Doughnuts

Heat milk until warm in a microwave oven, until lukewarm. Pour into bowl of a stand mixer fitted with dough hook. Add yeast and stir. Let stand for 10 min.

Beat in granulated sugar, butter, egg and salt. Add flour. Beat on medium-high until dough forms a ball and pulls away cleanly from the sides and bottom of the bowl, about 5 min.

Start the mixer on low speed with a dough hook to mix the dough until it comes away from the side of the bowl, about 2 - 3 minutes.

Brush a medium bowl with oil. Line a large baking sheet with parchment. Lightly brush with oil.

Scrape dough out of mixer bowl into oiled bowl. Lightly oil top of dough and cover with a damp tea towel (not terry cloth). Let stand in a warm place until dough doubles in size, about 1 hour. OR cover with plastic wrap directly onto the surface of the dough, cover the bowl with another sheet of plastic, leave in the fridge overnight.

Roll out dough on a floured surface to 1/2 to 3/4 in. thick. Using a 2.75-in. round cutter, cut into 20-24 rounds. Transfer to prepared sheet. Cover with same damp tea towel and let stand until doughnuts double in size, about 45 min.

Pour oil into a pot until it reaches 1 in. up the sides. Clip a deep-fry thermometer to the side. Heat over medium until temperature reaches 325F. Adjust heat as necessary to keep temperature at 325F during cooking. Fry doughnuts, 4 at a time, flipping halfway through, until golden, 2 to 3 min. Drain on paper towels.

When the doughnuts are completely cooled, poke a hole on the side of the doughnuts.

Fill a pastry bag with pastry cream fitted with a medium plain tip, or with a bismark tip if you have one.

Caramel Glaze
Place sugar in a small saucepan, wet it with about a tablespoon of water, let it cook until it reaches a light honey colour, take off heat right away, the caramel with continue to darken more.
Let caramel cool for a little, about a minute or so, carefully dip each doughnut top into the caramel, holding the sides of the doughnut. *the caramel is very hot, so use caution!
Let the excess caramel drip down, and place it on a rack, caramel side up, continue with the rest the doughnuts. They are ready to serve once the caramel glaze has hardened.